How can I sub divide an equilateral triangle into many smaller equilateral triangles
I could not yet figure out how to do it procedurally or in a non destructive manner. In the meantime you can easily do it by hand.

There is an addon shipped by default with Blender called Add Mesh: Extra Objects that can activated in the User Preferences dialog

Start by opening File > User Preferences > Addons then search for Extra and activate the Add Mesh: Extra Objects addon.

Then in the 3D View press Shift+A > Add > Mesh > Math Function > Regular Solid. 

By default it should already create a Tetrahedron, if not just pick it from the pulldown preset menu.

The just enter Edit Mode, select all faces, press W > Subdivide. Adjust Subdivision Number from the operator properties in the Toolshelf, or pressing F6